Actually tinning the wire isn't good unless you have spring terminals. The solder will cold flow from the force and will loosen up the screw terminal connection. You probably had the small blue wire loose since it is a smaller gauge wire. The screw terminal touched the larger gauge wire first and you didn't get any compression on the blue wire. That wire connection had high resistance and heated.
Get wire ferrules to keep the wire ends neat instead of solder and be careful putting different gauges in the same spot. If you can stack them vertical they will both get compressed, but side by side won't work.